A230549 Coins left after packing twin hearts patterns into n X n coins.

4, 5, 8, 13, 12, 21, 32, 33, 40, 57, 48, 69, 84, 85, 96, 125, 108, 141, 160, 161, 176, 217, 192, 237, 260, 261, 280, 333, 300, 357, 384, 385, 408, 473, 432, 501, 532, 533, 560, 637, 588, 669, 704, 705, 736, 825, 768, 861

Offset

2,1

Comments

Twin hearts (6c4a type) is one of total 17 distinct patterns appearing in 3X2 coins where each pattern consists of 6 perimeter parts from each coin and forms a continuous area.

a(n) is total coins left after packing twin hearts patterns (6c4a type: 6-curves cover 4 coins) into n X n coins with rotation not allowed. The total twin hearts patterns is A230548 and voids left is A230550. See illustration in links.

Links

Table of n, a(n) for n=2..49.

Kival Ngaokrajang, Illustration of initial terms (U)

Formula

a(n) = n^2 - 4*A230548(n).

G.f.: x^2 * (-3*x^10 - 4*x^8 + 3*x^7 + 8*x^6 + 4*x^5 - x^4 + 4*x^3 + 4*x^2 + 5*x + 4)/(1+x^3)*(1-x^3)^2*(1-x^2). (conjectured). - Ralf Stephan, Oct 30 2013

Prog

(Small Basic)
 col = 1
row = 0
For n = 2 To 100
  add = 0
  If Math.Remainder(n, 2) * Math.Remainder(n, 3) <> 0 Then
    add = 1
  EndIf
  If n >= 4 And Math.Remainder(n, 2) = 0 Then
    col = col + 1
  EndIf
  If n >= 3 And Math.Remainder(n, 3) = 0 Then
    row = row + 1
  EndIf
  U = n * n - (col * row + add)*4
  TextWindow.Write(U+", ")
EndFor

Crossrefs

Cf. A008795, A230370 (3-curves); A074148, A227906, A229093, A229154 (4-curves); A001399, A230267, A230276 (5-curves); A229593, A228949, A229598, A002620 (6-curves).

Sequence in context: A061765 A242274 A297419 * A133940 A174398 A341420

Adjacent sequences: A230546 A230547 A230548 * A230550 A230551 A230552

Keyword

nonn

Author

Kival Ngaokrajang, Oct 23 2013

Status

approved